Analysis & PDE · Mathematics & Statistics
Analysis of PDEs
The newest papers in Analysis of PDEs that ReadSearch has read, newest first. Each links to its own page, with its authors, date, where it was published and the original.
37 papers, from 10 September 2026 to 5 November 2026: 37 arXiv preprints.
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Newest papers, page 2
The Symbol of the Surrogate: Measuring Numerical Provenance in Neural PDE Solvers
Neural PDE surrogates are trained on numerical solver outputs that contain both physical evolution and solver-specific discretization errors.Barron Optimal Transport I: Generative Modeling
Motivated by recent applications in generative modeling and sampling, we introduce a framework for optimal measure transport where cost captures the notion of neural network complexity.A Neural JKO Scheme for Hellinger-Kantorovich Gradient Flows via Monge-Growth Pairs
We develop a mesh-free neural JKO scheme for advection-reaction-diffusion equations with a gradient-flow structure in the Hellinger-Kantorovich (HK) geometry of unbalanced optimal transport.Navier-Stokes lost in translation: Why Lean verification of AI autoformalisation does not guarantee correct natural language proofs
Autoformalisation is increasingly used to verify mathematical texts, including those generated by AI, as in OpenAI's announced proof of blow-up of solutions to the Navier-Stokes equations.Rapid Fredholm stabilization of the Kuramoto--Sivashinsky equation with unrestricted, spatially-varying anti-diffusion
We develop the first feedback design for rapid stabilization of the Kuramoto--Sivashinsky equation with a spatially varying anti-diffusion coefficient.On prediction from expert advice with more than five experts
We prove that no single rank ordered adversary strategy is globally optimal for the prediction with expert advice problem with six or more experts, in both the geometric stopping and finite time…Quantum Optimal Transport Barycenters: Existence, Duality, and Gaussian Rigidity
We develop a Quantum Optimal Transport (QOT) barycenter framework for quantum states, as an analog of Wasserstein barycenters~\cite{AguCar}, and establish existence and duality results for a broad…Densities for scalar-valued BSDEs via unique continuation and backward uniqueness
We give sufficient conditions ensuring that, at every fixed positive time, the scalar backward component of a Markovian forward-backward stochastic differential equation with multidimensional…The finite-horizon five-expert prediction problem
We give an explicit solution to the five expert prediction with expert advice partial differential equation (PDE) in the finite-time horizon setting.Sparse-Observation Atmospheric Thermal Forecasting with Physics-Informed Neural Networks for Climate-Aware Digital Twins
Short-horizon forecasts of atmospheric temperature are needed to support climate-aware digital-twin systems, but such forecasts must be produced where thermal observations are incomplete.Sharp Convergence of Wasserstein Gradient Flows for Spectrally Nonnegative Interaction Energies
We study the long-time behavior of Wasserstein gradient flows for interaction energies \[ \mathsf E[μ] = \frac12\iint_{M\times M}K(x,y)\,\mathrm dμ(x)\,\mathrm dμ(y) \] on a closed manifold $M$.Learning Lyapunov Operators for Nonlinear Systems
Constructing Lyapunov functions for nonlinear dynamical systems is a central problem in stability analysis, yet remains challenging.An explicit solution of the five-expert prediction PDE and the exact optimality set of COMB
In this paper, we derive an explicit solution of the stationary prediction with expert advice PDE for five experts.Linearized PINN with pretrained nonlinear layers
We propose a linearized Physics-Informed Neural Network (lPINN), a reduced-order neural basis method for forward and inverse differential equations.Volumetric Harmonic Field Navigation for Quadrotors
Quadrotor navigation in cluttered 3-D environments requires global guidance while local motion remains subject to collision and motion limits.Quantitative Diffusive Limits for Singular Nonlocal Transport
We study the nonlocal continuity equation \[ \partial_tμ_b =\operatorname{div}\!\left( μ_b\nabla\log\bigl((I-b^2Δ)^{-1}μ_b\bigr) \right) \] on a closed connected Riemannian manifold.Score-based Outlier Generation via Controlling the Radon-Nikodym Derivative
Outliers are important for stress-testing algorithms and understanding system behaviour under rare conditions.